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updated docs of GP formula fn to include more details on hyperparameters #1726

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jr-leary7
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in response to #1725, i added some further documentation on the hyperparameters estimated by a GP, specifically the length-scale $\ell$ and the marginal standard deviation $\sigma$, including general guidelines on how to interpret each hyperparameter.

what remains is to add the name, support, and simple interpretation of the hyperparameter $z$ to the relevant table in the roxygen2 doc section of gp(), as this bit is unclear to me. i left the two cells in the table that i was unable to fill in marked with ???. i would also appreciate if someone gave a quick look over the information i've provided to ensure correctness, though i mostly took the info straight from the MC-Stan docs and forums.

@paul-buerkner
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Great, thanks! I will take a closer look and merge it before the next release.

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@avehtari avehtari left a comment

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couple fixes as comments

@@ -64,6 +64,30 @@
#' \url{https://mc-stan.org/docs/functions-reference/matrix_operations.html}
#' under "Gaussian Process Covariance Functions".
#'
#' There are several parameters estimated by the GP, the most important of which
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by the GP -> for the GP

#' \code{sd} \tab \eqn{\sigma} \tab \eqn{\mathbb{R}^+} \tab marginal standard deviation of the GP's covariance kernel \cr
#' \code{z} \tab \eqn{z} \tab ??? \tab ??? \cr
#' }
#' Assuming an exponential quadratic covariance structure, the parameters
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exponential -> exponentiated

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